基于混合谱数据的不连续Sturm-Liouville逆谱问题局部可解性和稳定性

Local Solvability and Stability of the Inverse Spectral Problems for the Discontinuous Sturm-Liouville Problem with the Mixed Given Data

该文研究有限区间(0,1)上具有Robin边界条件和不连续点x=d∈(0,12]的Sturm-Liouville算子逆谱问题.假设已知的数据为一组子谱、势函数在(d,1)上的信息以及右边界条件和不连续条件中的部分参数,该文证明恢复(0,d)上的势函数和左边界条件参数的逆谱问题局部可解性和稳定性,其中已知的势函数信息和右边界条件参数允许存在一定的误差.

This paper studies inverse spectral problems for the Sturm-Liouville operator on(0,1)with the Robin boundary conditions and a discontinuity at x=d∈(0,12].Suppose that the known data contains one subspectrum,the potential function on(d,1)as well as partial parameters in the right boundary condition and the discontinuous conditions.The paper proves the local solvability and stability for the inverse problems of recovering the potential function on(0,d)and the parameter in left boundary condition,where the known potential and the parameter in the right boundary condition are allowed to contain errors.